منابع مشابه
Extremal Hypergraphs for Ryser’s Conjecture I: Connectedness of Line Graphs of Bipartite Graphs
Ryser’s Conjecture states that any r-partite r-uniform hypergraph has a vertex cover of size at most r− 1 times the size of the largest matching. For r = 2, the conjecture is simply König’s Theorem. It has also been proven for r = 3 by Aharoni using a beautiful topological argument. This paper is the first part of the proof of a characterization of those 3-uniform hypergraphs for which Aharoni’...
متن کاملCATEGORY OF (POM)L-FUZZY GRAPHS AND HYPERGRAPHS
In this note by considering a complete lattice L, we define thenotion of an L-Fuzzy hyperrelation on a given non-empty set X. Then wedefine the concepts of (POM)L-Fuzzy graph, hypergraph and subhypergroupand obtain some related results. In particular we construct the categories ofthe above mentioned notions, and give a (full and faithful) functor form thecategory of (POM)L-Fuzzy subhypergroups ...
متن کاملExtremal Hypergraphs for Ryser’s Conjecture: Connectedness of Line Graphs of Bipartite Graphs
In this paper we consider a natural extremal graph theoretic problem of topological sort, concerning the minimization of the (topological) connectedness of the independence complex of graphs in terms of its dimension. We observe that the lower bound dim(I(G)) 2 − 2 on the connectedness of the independence complex I(G) of line graphs of bipartite graphs G is tight. In our main theorem we charact...
متن کاملOn Diameter of Line Graphs
The diameter of a connected graph $G$, denoted by $diam(G)$, is the maximum distance between any pair of vertices of $G$. Let $L(G)$ be the line graph of $G$. We establish necessary and sufficient conditions under which for a given integer $k geq 2$, $diam(L(G)) leq k$.
متن کاملPartial line directed hypergraphs
The partial line digraph technique was introduced in [7] in order to construct digraphs with a minimum diameter, maximum connectivity, and good expandability. To find a new method to construct directed hypergraphs with a minimum diameter, we present in this paper an adaptation of that technique to directed hypergraphs. Directed hypergraphs are used as models for interconnection networks whose v...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1977
ISSN: 0012-365X
DOI: 10.1016/0012-365x(77)90127-3